The present invention relates to a transistor circuit and, more particularly, to an oscillation circuit which is capable of performing a stable oscillation against a wide range of temperature change.
As shown in FIG. 1, a conventional oscillation circuit is constituted by a differential amplifier 1 which is supplied with a positive feedback signal S.sub.F and which outputs an oscillation signal S.sub.0, and a feedback circuit 2 which is supplied with the oscillation signal S.sub.0. The differential amplifier 1 is constituted by a pair of transistors Q1 and Q2, a load Z.sub.L, a constant current source I, bias resistors R1 and R2, a bypass capacitor C3, and a bias voltage source V.sub.B. The feedback circuit 2 is constituted by coupling capacitors C1 and C2, and a resonance circuit composed of a capacitor C.sub.0 and an inductor L.sub.0.
In the following, the operation of the conventional oscillation circuit having the above circuit construction is described. When an oscillating current is produced in the oscillation circuit, the current is resonated through the resonance circuit composed of the capacitor C.sub.0 and the inductor L.sub.0 with a resonance frequency f expressed as follows. ##EQU1## The resonant current is then fed to the base of the transistor Q1 through the coupling capacitor C2, and amplified by the differential amplifier 1, so that an oscillation signal S.sub.0 is outputted from the collector of the transistor Q2 and then positively fed back to the base of the transistor Q1 through the coupling capacitors C1 and C2. As a result, oscillation with the same frequency as the resonance frequency is produced. That is, the oscillation frequency of the conventional oscillation circuit shown in FIG. 1 is expressed by the above equation (1). In the case of a high-frequency oscillation circuit, however, the oscillation frequency thereof cannot be expressed by the equation (1) because it is affected by the input impedance of the differential amplifier 1. The oscillation frequency of a high-frequency oscillation circuit is explained by making reference to the expressions given hereunder.
FIG. 2 shows the feedback circuit 2 extracted from the conventional oscillation circuit of FIG. 1 on the assumption that an input impedance of the differential amplifier 1 viewed from the base of the transistor Q1 is expressed by Z.sub.IN. In FIG. 2, the ratio V.sub.1 /V.sub.0, that is, a feedback factor .beta., is expressed as follows. ##EQU2## In the above expressions, S=j.omega., and G represents the reciprocal of the resistive component r of the coil L.sub.0.
When the open gain of the differential amplifier 1 is assumed to be represented by A.sub.0, a condition for oscillating is expressed by the following equation (4). EQU A.sub.0 .beta.=1 (4)
Applying the equation (4) into the equation (3), the following equation is obtained. ##EQU3##
If the imaginary part of .beta. is zero, the equation (5) is established and the oscillating condition is satisfied.
Here, ##EQU4##
Rearranging the equation (6) by substituting S=j.omega. thereinto, the following equation (7) is obtained. ##EQU5##
The oscillation frequency f.sub.0 of the circuit can be calculated according to the equation (7). In the equation (7), the input impedance Z.sub.IN of the differential amplifier 1 may be expressed by the following equation (8) on the assumption that it is pure resistance. EQU Z.sub.IN .apprxeq.h.sub.fe /g.sub.m ( 8)
in which g.sub.m represents the mutual conductance of the differential amplifier 1, and h.sub.fe represents the current amplification factor of the transistor concerned.
Substituting the above equation (8) into the equation (7), the following equation (9) is obtained. ##EQU6##
Thus, as expressed by the above equation (9), the oscillation frequency f.sub.0 of the conventional oscillation circuit contains the mutual conductance g.sub.m of the differential amplifier 1 expressed by the following equation (10). ##EQU7## in which k represents a Boltzmann constant, T represents an absolute temperature, and q represents an electron charge quantity.
From the above equation (10), it is understood that the mutual conductance g.sub.m changes as the temperature changes and, therefore, the oscillation frequency f.sub.0 including g.sub.m changes as the temperature changes. That is, the temperature-depending fluctuation of the oscillation frequency of the oscillation circuit is large. Here, the temperature-depending fluctuation of the oscillation frequency f.sub.0 is examined by substituting certain constants into the equation (9). Assuming now that G=0.001, h.sub.fe =100, g.sub.m =0.2 (at the temperature t=-25.degree.C.) and C.sub.0 =C.sub.1 =C.sub.2 are established and I does not change as the temperature changes, the oscillation frequency f.sub.1 at the temperature t=-25.degree. C. can be expressed by the equation (11). ##EQU8##
The mutual conductance g.sub.m ' at the temperature t'=75.degree. C. can be expressed by the following equation (12). ##EQU9##
Here, the value of g.sub.m ' at the temperature t'=75.degree. C. can be calculated by substituting 0.2 for g.sub.m as follows: EQU g.sub.m '.apprxeq.0.14
Accordingly, the oscillation frequency f.sub.2 at the temperature t'=75.degree. C. can be expressed as follows. ##EQU10##
Assuming now that f.sub.1 is 480 MHz, f.sub.2 =0.97 .times.480 =466 MHz. Accordingly, in a temperature range of from -25.degree. C. to 75.degree. C., the width of fluctuation of the oscillation frequency is 14 MHz. Thus, there has been a problem in that the temperature-depending fluctuation of the oscillation frequency is large.